Theorem 3.1 Hawkes Process Likelihood[1]}, [2]}
Let \(N(\cdot )\)  be a regular point processes on \([0,T]\)  for some finite positive \(T\)  and let \(t_1, t_2, ..., t_k\)  denote a realization of \(N(\cdot )\)  on \([0,T]\) . Then the likelihood \(L\)  of \(N(\cdot )\)  give a Hawkes process with intensity function \(\lambda (t)\)  is expressed in the following form.
\(L=\left[ \prod _{i=1}^k \lambda (t_i) \right]\exp \left( - \int _0^T \lambda (u) du \right)\) 

